Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{7 x^{2} + 6 x + 7}{- 4 x^{2} - 5 x + 9}

The limit is an indeterminate form of the type LaTeX: \displaystyle \frac{\infty}{\infty} . Using L'Hospitial's rule 2 times gives: LaTeX: \lim_{x \to \infty}\frac{7 x^{2} + 6 x + 7}{- 4 x^{2} - 5 x + 9} = \lim_{x \to \infty}\frac{14 x + 6}{- 8 x - 5} = \lim_{x \to \infty}\frac{14}{-8} = - \frac{7}{4}